Optimal coarsening of 3D reservoir models for flow simulation

We have developed a new constrained optimization approach to the coarsening of 3D reservoir models for flow simulation. The optimization maximally preserves a statistical measure of the heterogeneity of a fine-scale model. Constraints arise from the reservoir fluids, well locations, pay/nonpay juxtaposition, and large-scale reservoir structure and stratigraphy. The approach has been validated for a number of oil and gas projects, where flow simulation through the coarsened model is shown to provide an excellent approximation to high-resolution calculations performed in the original model. The optimal layer coarsening is related to the analyses of Li and Beckner (2000), Li et al. (1995), and Testerman (1962). It differs by using a more accurate measure of reservoir heterogeneity and by being based on recursive sequential coarsening instead of sequential refinement. Recursive coarsening is shown to be significantly faster than refinement: the cost of the calculation scales as (NX.NY.NZ) instead of (NX.NY.NZ)(2). The more accurate measure of reservoir heterogeneity is very important; it provides a more conservative estimate of the optimal number of layers than the analysis of Li et al. The latter is shown to be too aggressive and does not preserve important aspects of the reservoir heterogeneity. Our approach also differs from the global methods of Stern and Dawson (1999) and Durlofsky et al. (1996). It does not require the calculation of a global pressure solution, nor does it require the imposition of large-scale flow fields, which may bias the analysis (Fincham et al. 2004). Instead, global flow calculations are retained only to validate the reservoir coarsening. Our approach can also be used to generate highly unstructured, variable-resolution computational grids. The layering scheme for these grids follows from the statistical analysis of the reservoir heterogeneity. Locally variable resolution follows from the constraints (reservoir structure, faults, well locations, fluids, pay/ nonpay juxtaposition). Our reservoir simulator has been modified to allow a fine-scale model to be initialized and further coarsened at run time. This has many advantages in that it provides both simplified and powerful workflows, which allow engineers and geoscientists to work with identical shared models.